Mejane, Olivier Upper bound of a volume exponent for directed polymers in a random environment. (English) Zbl 1041.60079 Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 3, 299-308 (2004). Summary: We consider the model of directed polymers in a random environment introduced by Petermann: the random walk is \(\mathbb R^d\)-valued and has independent \(\mathcal N(0,I_d)\)-increments, and the random medium is a stationary centered Gaussian process \((g(k,x), k\geqslant 1, x \in \mathbb R^d)\) with covariance matrix cov\((g(i,x),g(j,y))=\delta_{ij}\Gamma(x-y)\), where \(\Gamma\) is a bounded integrable function on \(\mathbb R^d\). For this model, we establish an upper bound of the volume exponent in all dimensions \(d\). Cited in 17 Documents MSC: 60K37 Processes in random environments 60G42 Martingales with discrete parameter 82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) Keywords:directed polymers in random environment; Gaussian environment × Cite Format Result Cite Review PDF Full Text: DOI arXiv Numdam EuDML